# The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

Studia Mathematica (1992)

- Volume: 101, Issue: 3, page 285-298
- ISSN: 0039-3223

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topLu, Shanzhen, and Yang, Dachun. "The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space." Studia Mathematica 101.3 (1992): 285-298. <http://eudml.org/doc/215906>.

@article{Lu1992,

abstract = {We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.},

author = {Lu, Shanzhen, Yang, Dachun},

journal = {Studia Mathematica},

keywords = {Herz space; Littlewood-Paley function; new Hardy space; - transform},

language = {eng},

number = {3},

pages = {285-298},

title = {The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space},

url = {http://eudml.org/doc/215906},

volume = {101},

year = {1992},

}

TY - JOUR

AU - Lu, Shanzhen

AU - Yang, Dachun

TI - The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

JO - Studia Mathematica

PY - 1992

VL - 101

IS - 3

SP - 285

EP - 298

AB - We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.

LA - eng

KW - Herz space; Littlewood-Paley function; new Hardy space; - transform

UR - http://eudml.org/doc/215906

ER -

## References

top- [1] Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278. Zbl0677.30030
- [2] C. Fefferman and E. M. Stein, ${H}^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
- [3] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, Lecture Notes in Math. 1302, Springer, 1988, 223-246. Zbl0648.46038
- [4] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
- [5] J. García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513.
- [6] C. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform, J. Math. Mech. 18 (1968), 283-324.
- [7] D. S. Kurtz, Littlewood-Paley operators on BMO, Proc. Amer. Math. Soc. 99 (1987), 657-666.
- [8] S. Lu and D. Yang, Some new Hardy spaces associated with the Herz spaces, to appear. Zbl0782.42019
- [9] A. Torchinsky, Real-variable Methods in Harmonic Analysis, Academic Press, New York 1986.
- [10] D. Yang, The boundedness of generalized Littlewood-Paley functions, Chinese Ann. Math. Ser. A 12 (1991), 736-744. Zbl0758.42013

## Citations in EuDML Documents

top- Dachun Yang, Some new Hardy spaces $L\xb2{H}_{R}^{q}\left(\mathbb{R}{\xb2}_{+}\times \mathbb{R}{\xb2}_{+}\right)$ (0 < q ≤ 1)
- Shan Lu, Da Yang, The local versions of ${H}^{p}\left({\mathbb{R}}^{n}\right)$ spaces at the origin
- Lixia Liu, Bolin Ma, Sanyang Liu, The Fourier integral operators on Hardy spaces associated with Herz spaces

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